Examining the value of the secondary assist

[Hockey Outsider]

There's been a lot of talk over the past few years about secondary assists. I wanted to examine the data and understand the predictive values of goals, primary assists, and secondary assists. We intuitively think that goal-scoring and playmaking are innate talents, which are relatively stable from year to year - but I wanted to understand how the data looks when it's closely examined.

The key to this analysis is getting pairs of data for YEAR and YEAR+1. In other words, if we have information about how many goals, primary assists, and secondary assists a player scored in, say, 2014, can we estimate how many goals, primary assists and secondary assists a player recorded in 2015?

I looked at data from the 2008 to 2019 regular seasons - but we have to set up our parameters. There are going to be significant fluctuations in players' stats from year to year. Some of these I've controlled for, and some of these I haven't. All the data that I've analyzed is on a per-minute basis, to avoid distortion due to changes in games played and/or ice time. Three additional filters that I've applied:

• I'm only looking at data for forwards. From a first glance at the data, it was obvious that forwards and defensemen recorded primary assists at nearly the same rate; forwards recorded far more goals, and defensemen recorded far more secondary assists. To avoid distortion, I'm only looking at forwards.
• I'm only looking at even-strength scoring. No, I'm not one of those people who think that a powerplay points counts for less than an even-strength point. But I think that PP deployment materially impacts a player's results, and this can skew the numbers if it isn't properly accounted for. (I also want to be clear that the filter is even-strength - not necessarily five-on-five).
• I'm only looking at players who have at least 900 minutes in both seasons (ie at least 900 ES minutes in YEAR, and at least 900 ES minutes in YEAR+1). Data for a player-season is discarded if it fails to meet both criteria. The 900 minute threshold is admittedly arbitrary - I wanted a high enough threshold to filter out fluky data from small sample sizes, but low enough that I'd still end up with over a thousand data points.

Obviously, there are a number of factors that I haven't attempted to control for - age (generally speaking, we'd expect someone who's 19 to post better number in YEAR+1 than someone who's 39); quality of linemates; role on team; and just plain luck. Given that I have more than 1,200 data pairs, I'm confident that these matters will, on average, offset.

Before going further, we have to validate the data - if our starting point is flawed, then all of the following analysis is worthless. I obtained all of my data from naturalstattrick.com. I did a limited amount of spot-checking. For example, NHL.com shows that Kane has 324 ES assists going back to 2008. That's exactly the same number as what my database has. Unfortunately NHL.com doesn't show the level of detail I need (primary vs second assists at even strength). I looked at Kane's 2016 (Hart & Art Ross) season, and manually went through his scoring logs. I counted 23 ES goals, 28 ES primary assists, and 12 ES secondary assists. This is identical to the breakdown in my database. Based on the spot-checking that I've done (and this has to be done by spot-checking, since there are more than 10,000 lines of data), I'm satisfied that the data I'm using is a reasonable starting point.

Click to read more...

 

[Hockey Outsider]

This table shows the inter-year correlation between ES goals for forwards (subject to the parameters I discussed above). In other words, this attempts to answer the question - if we know how many ES goals per minute a forward scores in YEAR, how accurately can we predict the ES goals he'll score per minute in YEAR+1? The answer, as you can see, is not very well. The R^2 value (which explains how much of one data set explains another) is only 0.16, which is pretty low as far as these types of correlations go. There's definitely a relationship between the two sets of data (represented by the dotted red line), but the data is generally spread all over the place, so the correlation is weak. I'm not saying that goal-scoring isn't a repeatable skill - it definitely is - but I was surprised when I saw how weak the mathematical relationship was.

Moving on to primary assists, we see that the correlation is 0.16. If you drill down to four decimal places, you'll see that the inter-year correlation between goals, and inter-year correlation between assists, is identical. I don't think this is too surprising. When people think of primary assists, they tend to think of skilled playmakers who had an integral part in setting up the goal. It makes perfect sense to me that the correlation between goals and primary assists is virtually identical - I don't think that one skill is inherently more repeatable (or more valuable) than the other.

Here's the table for everyone's favourite - secondary assists. What jumps out is how weak the relationship is year-over-year. A correlation of zero means that there's no relationship between the two data sets. The data here isn't quite random, but it's only a small step above that. Before everyone demands that we discard secondary assists, let's look at the next table.

This table shows the inter-year correlation for total assists. It looks pretty similar to the goals table, but one thing that jumps out is the R^2 value is higher here, at 0.19. That's still a fairly low number, but I found it somewhat surprising that there's a stronger year-to-year correlation between assists than goals. The other thing that's interesting here is the inter-year correlation for total assists is higher than the inter-year correlation for primary assists. This suggests that, even though secondary assists obviously have little predictive value on their own, they seem to have some predictive value when combined with primary assists.

The penultimate table shows the inter-year correlation for primary points (that is, goals plus assists). The R^2 value is 0.19 here, which is higher than anything that we've seen so far (though still pretty low in the world of data analysis). This suggests that, although there's certainly some predictive value in goals and primary assists in isolation, looking at the entire offensive package will give you better, more predictive information.

Finally, let's look at points - which, going back more than a century, has been the NHL's primary metric for measuring offensive performance. The correlation here is 0.19 which (if you look to a 3rd decimal point) is the strongest correlation that we've seen so far. Again, this suggests that, while secondary assists have limited predictive value on their own, when combined with goals and primary assists, they become better at predicting future performance.

To sum up what these tables tell me - secondary assists, on their own, seem to have almost no predictive value. But, secondary assists have value because using total assists is better at predicting future performance than solely using primary assists. I dug deeper to figure out why, and I think I have an explanation. There's actually a fairly good correlation between secondary assists in YEAR, and total assists in YEAR+1. In other words, if I'm trying to estimate next year's secondary assists based on this year's secondary assists, I'm practically guessing. But, if I'm trying to estimate next year's total assists, based on the this year's secondary assists, there's some value there. Intuitively, this makes sense. A player who records a secondary assist is, on average, more involved in the play than someone who records no assists at all. So, by knowing how many secondary assists a player records this year, that probably gives me a good ballpark as to how involved he is in his team's offense - that on its own is a decent predictor of next year's success, and when it's combined with primary assists, we have a strong relationship still.

 

[Hockey Outsider]

So far we've just looked at correlations. I've shown some graphs, but I haven't done anything deeper. Without turning this into a math lesson, I'm going to turn to linear programming. This is a tool that allows you to maximize a number, by changing variables, subject to certain constraints. In this case, I attempted to maximize the correlation between 1) ES data for YEAR, applying different weightings to goals, primary assists, and secondary assists and 2) ES data in YEAR+1. The strongest correlation I could get in the data set (0.20 - stronger than anything we saw in the previous set of tables) occurred when goals were given a weighting of 1, primary assists were also given a weighting of 1, and second assists were given a weighting of approximately 0.66. (There were a few really wonky samples that skewed the formula - I recalculated after dropping the ten biggest positive and ten biggest negative outliers - probably not valid statistically - but the formula results didn't change in a meaningful way).

I then did a similar analysis using linear regression (which, despite having a similar name, is different from linear programming). It's the same general concept though - you're using variables, which are assigned different weights, to predict the results of a known number. (In other words, we're using goals, primary assists, and secondary assists, each with a different weighting, in YEAR, to predict total points in YEAR+1). This one actually suggests that primary assists have higher predictive value than goals (that is, the weight assigned to primary assists is higher than the weight assigned to goals). However I think the results of the first approach are more reasonable, as reviewing the output leads me to believe (for reasons I can't quite articulate) that linear regression isn't an appropriate mathematical technique here. The results of the previous analysis are also consistent with all the tables we saw previously.

 

[Hockey Outsider]

Let's put this all together. Based on all of this analysis, I think it's reasonable to argue that goals and primary assists have very nearly the same value. Based on the previous results, let's count primary assists as equal to goals, and secondary assists at 0.66 of the value.

This table shows the top 50 forwards, in ES scoring, from 2008 to 2019, based on total points, then adjusted points. I'm also showing how they rank overall:

Player	G	1A	2A	TOTAL	RANK	WEIGHTED	RANK	CHANGE
Sidney Crosby	261	260	132	653	1	608.12	1	-
Alex Ovechkin	347	184	103	634	2	598.98	2	-
Patrick Kane	256	246	131	633	3	588.46	3	-
Evgeni Malkin	228	234	105	567	4	531.3	4	-
Ryan Getzlaf	158	233	160	551	5	496.6	5	-
Eric Staal	222	190	111	523	6	485.26	6	-
Anze Kopitar	200	197	125	522	7	479.5	9	- 2
Jonathan Toews	230	185	105	520	8	484.3	7	1
Phil Kessel	242	180	94	516	9	484.04	8	1
Nicklas Backstrom	157	211	147	515	10	465.02	10	-
Joe Thornton	131	236	142	509	11	460.72	11	-
Henrik Sedin	117	215	176	508	12	448.16	15	- 3
Blake Wheeler	189	198	105	492	13	456.3	13	-
Corey Perry	239	170	74	483	14	457.84	12	2
Steven Stamkos	241	162	76	479	15	453.16	14	1
Daniel Sedin	182	195	101	478	16	443.66	17	- 1
David Krejci	146	210	114	470	17	431.24	18	- 1
John Tavares	222	172	76	470	17	444.16	16	1
Henrik Zetterberg	163	188	107	458	19	421.62	19	-
Jamie Benn	195	131	131	457	20	412.46	23	- 3
Claude Giroux	157	181	114	452	21	413.24	21	-
Joe Pavelski	215	147	88	450	22	420.08	20	2
Zach Parise	213	137	95	445	23	412.7	22	1
Jason Pominville	185	156	102	443	24	408.32	24	-
Jarome Iginla	205	151	76	432	25	406.16	25	-
Thomas Vanek	190	160	81	431	26	403.46	26	-
Jakub Voracek	145	183	101	429	27	394.66	28	- 1
Patrice Bergeron	174	155	98	427	28	393.68	29	- 1
Rick Nash	232	125	65	422	29	399.9	27	2
Paul Stastny	149	163	109	421	30	383.94	33	- 3
Jeff Carter	214	118	87	419	31	389.42	30	1
Patrick Marleau	214	112	89	415	32	384.74	32	-
Matt Duchene	177	150	88	415	32	385.08	31	1
Loui Eriksson	169	134	109	412	34	374.94	38	- 4
Jason Spezza	164	162	86	412	34	382.76	34	-
Brad Marchand	186	133	90	409	36	378.4	36	-
Bobby Ryan	183	141	80	404	37	376.8	37	-
Martin St. Louis	153	143	104	400	38	364.64	41	- 3
Tyler Seguin	186	151	63	400	38	378.58	35	3
Andrew Ladd	183	125	91	399	40	368.06	39	1
Milan Lucic	159	143	96	398	41	365.36	40	1
David Backes	167	117	105	389	42	353.3	42	-
Mike Ribeiro	112	171	103	386	43	350.98	44	- 1
Justin Williams	151	118	115	384	44	344.9	46	- 2
Mikko Koivu	120	131	126	377	45	334.16	50	- 5
Chris Kunitz	157	133	86	376	46	346.76	45	1
Dustin Brown	166	138	72	376	46	351.52	43	3
Marian Hossa	176	109	85	370	48	341.1	48	-
Pavel Datsyuk	133	147	89	369	49	338.74	49	-
Bryan Little	149	138	82	369	49	341.12	47	2

[TBODY] [/TBODY]

Despite the thousands of posts that have been written about secondary assists, even if we discount them to an appropriate value, the scoring race hardly changes. Crosby remains the leader in even-strength scoring (those his lead over Ovechkin plummets from 3.0% to 1.5%). The top ten scorers are identical (with Kopitar falling two spots and Toews and Kessel rising one spot each as a result). The top 25 players are the same; 23 of them change no more than two spots in the rankings.

(You can also cross-refer the data from here to the official results on NHL.com. Many of the players have the same data, but there are some small discrepancies - Ovechkin, for example, has 2 more ES points on NHL.com. There are actually quite a few players whose results are off by one or two points - but I'd dismiss that as an immaterial difference over the span of eleven seasons' worth of hockey).

 

[Bear of Bad News]

I'm surprised that (at least in the data set that you used) the r^2 for goals and primary assists is identical to four decimal places.

 

[Hockey Outsider]

I'm surprised that (at least in the data set that you used) the r^2 for goals and primary assists is identical to four decimal places.

I checked that at least five times - it's such an unlikely coincidence for it to be the same number to so many decimal points. (I haven't posted the results, but goal-scoring seems to be a fair bit more predictive for defensemen, compared to primary assists).

I realize, of course, you're not implying that I'm fudging the numbers, but I'm happy to share the data I've posted with anyone who wants a copy.

 

[Bear of Bad News]

I've known you long enough to know that you're not fudging the numbers.

 

[Hockey Outsider]

One point to add - this article is loosely based on one from 2011 -
Simplify scoring: drop the pointless secondary assist. I used a fairly similar approach to the author of that study.

I found lower correlations for goals and primary assists than that author did. I found a higher correlation for secondary asissts, but it's really low in both cases.

How do I explain the different results? Part of it is because I used a much larger set of data (11 seasons; he used three). I'm also using a higher threshold for minutes (900 ES minutes; he's using 60 games played) - which potentially weeds out smaller data points. But I don't know if that explains everything - curious to hear if anybody has ideas.

 

[Vujtek]

(You can also cross-refer the data from here to the official results on NHL.com. Many of the players have the same data, but there are some small discrepancies - Ovechkin, for example, has 2 more ES points on NHL.com. There are actually quite a few players whose results are off by one or two points - but I'd dismiss that as an immaterial difference over the span of eleven seasons' worth of hockey).

I'm pretty sure than in most cases, and especially in Ovechkin's, that difference comes from penalty shot goals. Seems to me naturalstattrick isn't counting those towards ES goals/points.

Anyways good job with the study!

 

[Hockey Outsider]

I'm pretty sure than in most cases, and especially in Ovechkin's, that difference comes from penalty shot goals. Seems to me naturalstattrick isn't counting those towards ES goals/points.

Anyways good job with the study!

Thanks for the feedback, I think that explains the differences.

During this period, Ovechkin had two penalty shot goals, both of which were at ES - so NHL.com's numbers are 2 points higher than the numbers I got from naturalstattrick (see hockey-reference.com). Crosby and Kane, whose numbers are identical to NHL.com's, had zero penalty shot goals during this period. Staal had three penalty shot goals, 2 ES and 1 PP, and that explains the two point difference here. I'm not going to look at each player with a difference, but that explanation - naturalstattrick excludes penalty shot goals - fits the data.

 

[Midnight Judges]

First of all, nice work running the numbers.

In the article you linked, Eric T's most significant finding is what happens when a player changes teams - the goals and primary assists transfer with the player whereas the secondary assists basically do not.

This supports the theory that secondary assists reflect team and circumstance more than the individual. If this isn't true, then why would they not transfer when a player switches teams - same as goals and primary assists?

 

[Michael Farkas]

Usage and structure. It's not team randomness.

Good example off the top of my head, Drew Doughty. Kings power play setup in 2011 ran with Doughty exit/carry, Kopitar carry/entry, dish to Johnson -> shot, tip from Brown/Smyth. In 2012, in went around the horn to Justin Williams for a shot (better shooter option than deflected one-timer). Doughty was a big part of the power play, but there's no tertiary assists for him...in the last few years, the Kings were able to utilize Doughty's shot from the left, slide Jeff Carter towards the mid-slot...more central role to the finishing product, therefore more points.

Tactics, usage, and structure are necessary parts to understand. A three-line carrier is way more important than the bump back pass to the point after the entry. But bump back pass is gonna get the assist, not the carrier...that's life. That's why it's usually easier for one-dimensional wingers to pick up "primary points" because their more limited use to the team pushes them to the wings in the first place - the more important procedures are delegated to the more important positions as a general rule.

 

[Canadiens1958]

Short medium or stretch transition pass influences secondary assist values.

 

[Midnight Judges]

Nobody said anything about randomness.

 

[Michael Farkas]

Don't have to, implied with the team-to-team variability stake in the ground.

 

[Hockey Outsider]

First of all, nice work running the numbers.

In the article you linked, Eric T's most significant finding is what happens when a player changes teams - the goals and primary assists transfer with the player whereas the secondary assists basically do not.

This supports the theory that secondary assists reflect team and circumstance more than the individual. If this isn't true, then why would they not transfer when a player switches teams - same as goals and primary assists?

I didn't look at players that were traded for two reasons. One, it's a challenge to try to analyze the data properly that way. Two, I don't think the author's conclusion really changed - the year-over-year correlation for primary assists is very similar, regardless of if he's looking at traded players or everyone. The year-over-year correlation for secondary assists is close to zero in both cases.

I wouldn't go as far as saying that secondary assists have no value. There's clearly some value because it means, if nothing else, that the player who got the secondary assist was involved in the offense. Better to be involved and get a secondary assist, vs getting nothing at all. This is borne out in the fact that the correlations always improve when secondary assists are included.

That being said, I think this demonstrates that there's a fair bit of variability and secondary assists definitely should not have the same weighting as goals or primary assists.

 

[Jim MacDonald]

Hey everyone, if it's cool/ok to ask in this thread (as my google research didn't give me an answer). Does anyone happen to know either exactly or a "roundabout" year/years the NHL started awarding and scoring the second assist? Thank you in advance!-Jim

 

[morehockeystats]

Hey everyone, if it's cool/ok to ask in this thread (as my google research didn't give me an answer). Does anyone happen to know either exactly or a "roundabout" year/years the NHL started awarding and scoring the second assist? Thank you in advance!-Jim

at least since 1922:

1922020004

19221220

TSP 2 - 7 SEN

[TBODY] [/TBODY]

PUNCH BROADBENT (2) , ASSISTS: JACK DARRAGH (1), GEORGES BOUCHER (3)

 

[Jim MacDonald]

at least since 1922:

1922020004

19221220

TSP 2 - 7 SEN

[TBODY] [/TBODY]

PUNCH BROADBENT (2) , ASSISTS: JACK DARRAGH (1), GEORGES BOUCHER (3)

Thanks Morehockeystats!!

 

[Hockey Outsider]

Hey everyone, if it's cool/ok to ask in this thread (as my google research didn't give me an answer). Does anyone happen to know either exactly or a "roundabout" year/years the NHL started awarding and scoring the second assist? Thank you in advance!-Jim

@Canadiens1958 might be able to answer on the timing of the rule changes.

I've heard (but can't cite a source) that the NHL was, in theory, able to award three assists per goal back in the 1920's - but given how fewer assists were actually awarded in practice, this was probably an extremely rare occurrence.

In terms of stats - there were about 1.5 assists per goal in 1950. That increased steadily to about 1.7 assists per goal in 1980, and it's been remarkably consistent ever since.

 

[Vujtek]

@Canadiens1958 might be able to answer on the timing of the rule changes.

I've heard (but can't cite a source) that the NHL was, in theory, able to award three assists per goal back in the 1920's - but given how fewer assists were actually awarded in practice, this was probably an extremely rare occurrence.

In terms of stats - there were about 1.5 assists per goal in 1950. That increased steadily to about 1.7 assists per goal in 1980, and it's been remarkably consistent ever since.

I haven't come across an actual rule that would have prevented the awarding of secondary assists in the first few years of the NHL but the first time a goal was credited with two assists happened in 1922-23 season (happened seven times that season).

You're right that there was even years when tertiary assists were allowed and even awarded but it happened in the 1930's, not 20's. Per the rules apparently tertiary assists were possible from 1930-31 season onwards but they were actually awarded only during two years:

1934-35 (57 tertiary assists awarded)
1935-36 (65 tertiary assists awarded)

Since 1936-37 season only a maximum of two assists per goal were allowed.

 

[Canadiens1958]

Gradually the awarding of assists were liberalized. The chronological info above is accurate but has to be tempered with the definintion of assists. Initially direct pass, no partial deflected passes, no dump and chase, no rebound assists of any type.

 

[Jim MacDonald]

@Canadiens1958 might be able to answer on the timing of the rule changes.

I've heard (but can't cite a source) that the NHL was, in theory, able to award three assists per goal back in the 1920's - but given how fewer assists were actually awarded in practice, this was probably an extremely rare occurrence.

In terms of stats - there were about 1.5 assists per goal in 1950. That increased steadily to about 1.7 assists per goal in 1980, and it's been remarkably consistent ever since.

Wow......you know what blows me away Hockey Outsider....Thinking about how owner's were in such a tremendous general position of leverage (only six teams, the league not having a player's union yet).....I wonder if they gave out incentive-based contracts to players selling the "fallacy" of "If you get x many points, we'll give you x amount of money.....the league can award up to 3 assists on a goal, so this is a tremendous opportunity young man" knowing darn well these extra assists were given few and far between.....hmmmm

 

[Canadiens1958]

Wow......you know what blows me away Hockey Outsider....Thinking about how owner's were in such a tremendous general position of leverage (only six teams, the league not having a player's union yet).....I wonder if they gave out incentive-based contracts to players selling the "fallacy" of "If you get x many points, we'll give you x amount of money.....the league can award up to 3 assists on a goal, so this is a tremendous opportunity young man" knowing darn well these extra assists were given few and far between.....hmmmm

NHA, pre-NHL did not award assists because the ownersdid not want to pay extra for them.

 

[VoluntaryDom]

Usage and structure. It's not team randomness.

Good example off the top of my head, Drew Doughty. Kings power play setup in 2011 ran with Doughty exit/carry, Kopitar carry/entry, dish to Johnson -> shot, tip from Brown/Smyth. In 2012, in went around the horn to Justin Williams for a shot (better shooter option than deflected one-timer). Doughty was a big part of the power play, but there's no tertiary assists for him...in the last few years, the Kings were able to utilize Doughty's shot from the left, slide Jeff Carter towards the mid-slot...more central role to the finishing product, therefore more points.

Tactics, usage, and structure are necessary parts to understand. A three-line carrier is way more important than the bump back pass to the point after the entry. But bump back pass is gonna get the assist, not the carrier...that's life. That's why it's usually easier for one-dimensional wingers to pick up "primary points" because their more limited use to the team pushes them to the wings in the first place - the more important procedures are delegated to the more important positions as a general rule.

theres a reason people do these studies confined to even strength